@inproceedings{3d535924e0c94f1f991b37463a5e8636,

title = "An optimal generalization of the centerpoint theorem, and its extensions",

abstract = "We prove an optimal generalization of the centerpoint theorem: given a set P of n points in the plane, there exist two points (not necessarily among input points) that hit allconvex objects containingmore than 4n/7 points of P. We further prove that this bound is tight. We get this bound as part of a more general procedure forfinding small number of points hitting convex sets over P, yieldingseveral improvements over previous results.",

keywords = "Centerpoint theorem, Combinatorial geometry, Discrete geometry, Extremal methods, Hitting convex sets, Weak -nets",

author = "Nabil Mustafa and Saurabh Ray",

year = "2007",

doi = "10.1145/1247069.1247097",

language = "English (US)",

isbn = "1595937056",

series = "Proceedings of the Annual Symposium on Computational Geometry",

pages = "138--141",

booktitle = "Proceedings of the Twenty-third Annual Symposium on Computational Geometry, SCG'07",

note = "23rd Annual Symposium on Computational Geometry, SCG'07 ; Conference date: 06-06-2007 Through 08-06-2007",

}